river cruise starting in Bingen, but what do we do with the car

You can take the boat back, or you can take the train.

Take the train back. If you take the boat it will take you twice as long to get back as it did to get there. The train is cheaper than the boat too.

It's actually a little cheaper to take the boat round trip (Bingen to St. Goar and back, 21,60€) than one way on the boat (Bingen to St. Goar, 18,70€) plus train fare back (5,70€), but the time back by boat is 1h25m vs 37 min by train. I'm not sure where you would park in St. Goar, but if you started there and took the train to Bingen, then you would get a 20% discount (3,75€) on your boat ticket by showing the train ticket at the boat ticket kiosk. Find fares on K-D.de (http://www.k-d.com/en/kd-scheduled-cruises/day-cruise-rates/#c620) and click on "transferring between ship and train" at bottom of page.

"...we are traveling from the south of Germany..." For the best advice on how to do this, tell us where you're starting from and where you're staying that night, and provide the date in question. Generally, travel with the current (south to north) and don't return by boat (which takes 50% longer than the trip north and is terribly redundant.)

Before you plan a "couple hours", look at Rick's "Germany". He makes a convincing case that you only need Bingen to Boppard. (What we did.) You might even get a group ticket or some kind of train discount, especially on weekends. Download a boat schedule, and you'll see that there are only a few a day in each direction, anyway. The trains are frequent and fast enough, even the locals. You might want to stop somewhere else with the car for a meal or more sightseeing, either a castle visi or Deutsches Eck, for example. There are a million things to do along the Rhine.

If you are 60 and over, the KD boat is -30%, but you can't combine it with the train ticket discount.